Stability criteria hydrodynamic

For the hydrodynamic instability model, Lienhard and Dhir (1973b) extended the Zuber model to the CHF on finite bodies of several kinds (see Sec. 2.3.1, Fig. 2.18). Lienhard and Hasan (1979) proposed a mechanical energy stability criterion The vapor-escape wake system in a boiling process remains stable as long as the net mechanical energy transfer to the system is negative. They concluded that there is no contradiction between this criterion and the hydrodynamic instability model. 

A few words on the stability of steady states of polymerization. This question arises immediately as soon as the multiplicity of steady-state conditions spears. It is well known that three solutions are possible in the flow of reactants. The general theory of thermal instability of reactors has been developed in detail in Refe. [16-20,30,31], and the theory of kinetic instability caused by peculiarities of the kinetic schenK (self-acceleration. gel-effect, etc. in Refs. [37-40]). The instability of steady states of poly-nKiization plug reactors of a hydrodynamic nature is more interesting for the present paper. It can be assumed that the state corresponding to the negative slopes of the P(Q) curve are unstable if P = const is maintained [30, 33, 34]. At Q = const, all states are stable and realizable. The analysis of this problem in zero-dimensional formulation [41], for a reactor determined by only one value of T, p, q and a complex variable hydrodynamic resistance has shown that the slope of the curve is not an exhaustive stability criterion. 

While a purely hydrodynamic source for turbulence has not yet been demonstrated, the situation is much different when MHD effects are considered in a shearing, Keplerian disk. In this case, the Rayleigh criterion for stability can be shown to be irrelevant provided only that the angular velocity of the disk decreases with radius, even an infinitesimal magnetic field will grow at the expense of the shear motions. 

The so-called potential can be taken as a first estimate for the surface potential. The potential is the electrostatic potential at the hydrodynamic shear plane close to the particle surface. It can be determined from electrophoretic mobility measurements of the particles in an electric field (see for example Ref. [23]). The potential is zero when the charge within the shear plane is zero. This is the case as the surface charge plus the charge due to adsorbed ions other than hydrogen (for example AIOH2 in the case of alumina suspensions) is zero. This point is the iso-electro-point (i.e.p.) of the material in the dispersion medium. The suspension pH with respect to the i.e.p. is an important criterion for a first judgement of possible electrostatic stability. 

For Taylor numbers exceeding Tc, the flow develops a secondary flow pattern in which ur and uz are both nonozero. A sketch of the stability criteria given by (3-86) is shown in Fig. 3 8. The reader who is interested in a detailed description of the stability analysis that leads to the criterion (3-86) is encouraged to consult Chap. 12 or one of the standard textbooks on hydrodynamic stability theory (see Chandrashekhar [1992] for a particularly lucid discussion of the instability of Couette flows).12... 

Consider now coalescence taking into account the molecular and electrostatic forces. Of the greatest interest is dependence of stability factor F on parameters k, //, Sa, Sr, t, y, a, and definition of the criterion for transition from slow to fast coagulation. In Section 11.5 the condition of transition from slow to fast coagulation was considered within the framework of DLVO theory of identical colloid particles without taking into account hydrodynamic interaction... 

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